# Z9–I–1

In all nine fields of given shape to be filled with natural numbers so that:

• each of the numbers 2, 4, 6, and 8 is used at least once,

• four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square,

• in the circle is the sum of the numbers of adjacent cells of the inner square.

Find out the smallest and the largest number that can be written in a circle.

• each of the numbers 2, 4, 6, and 8 is used at least once,

• four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square,

• in the circle is the sum of the numbers of adjacent cells of the inner square.

Find out the smallest and the largest number that can be written in a circle.

### Correct answer:

#### You need to know the following knowledge to solve this word math problem:

#### Themes, topics:

#### Grade of the word problem:

We encourage you to watch this tutorial video on this math problem: video1

## Related math problems and questions:

- Twenty

Twenty rabbits are put in 4 cells so that there are a different number of rabbits in each cell containing at least three rabbits. What is the largest possible number of rabbits in one cell? - Determine 5893

Determine the largest integer n for which the square table n×n can be filled with natural numbers from 1 to n² (n squared) so that at least one square power of the integer is written in each of its 3×3 square parts. - Difference 68664

The digits 1, 2, 4, and 8 form two four-digit numbers so that all 4 digits are used in the notation of each number. Calculate the difference between such largest even number and smallest odd number (in that order). - Restriction 7442

The figure shows two rows of hexagonal boxes that continue to the right without restriction. Fill in one field with one positive integer so that the product of the numbers in any three adjacent fields is 2018. Determine the number that will be in the top - Z9–I–4 MO 2017

Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of the three was equal to the sum of the remaining two. The conductor said - Different 7909

Kryštof sells 10 bells at different prices: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 euros. He needs to pack all the bells into 3 boxes so that the price of the bells in each box is the same. How many ways can he do this? A)1 b)2 c)3 d)4 e)cannot be divided in this - Natural numbers

Determine the number of all natural numbers greater than 200 in which the digits 1, 2, 4, 6, and 8 occur at most once each. - Half-planes 36831

The line p and the two inner points of one of the half-planes determined by the line p are given. Find point X on the line p so that the sum of its distances from points A and B is the smallest. - Four-digit 65124

Please find out how many different four-digit numbers we can create from the digits 3 and 8 so that the two digits three and two digits eight are used in each four-digit number created. - Different 66994

There are 180 balls in three different colors in the bag. What is the smallest number of marbles to be selected so that there are at least 3 of the same color among them if the marble of the same color is the same in all three colors? - Decide

The rectangle is divided into seven fields. On each box is to write just one of the numbers 1, 2, and 3. Mirek argues that it can be done so that the sum of the two numbers written next to each other is always different. Zuzana (Susan) instead argues that - Smallest 4692

A. Find the largest natural number by which the numbers 54 and 72 can be divided (120, 60, and 42) B. Find the smallest natural number that can be divided by each of the numbers 36 and 48 (24,18 and 16) - Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than one so that the proportions R:A, R:B are with the remainder 1. - Metal balls

Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level? - Repeated 38103

How many 5-digit numbers can we assemble from the number 2,3,4,5,6,7,8,9 if the digit in each number can be repeated only once? - Indistinguishable 81481

How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice. - Guaranteed 37611

Determine how many different ways a Lotto ticket can be written if we guess six numbers out of 49. At what Jackpot would it already pay to bet so many tickets to be guaranteed to win the 1st prize? The price of one type is €1.